ACTIVE FILTERS

ELECTRIC CIRCUITSEIGHTH EDITION

JAMES W. NILSSON&SUSAN A. RIEDEL

CHAPTER 15ACTIVE FILTER CIRCUITS 2008 Pearson Education

CONTENTS

15.1 First-Order Low-Pass and High-Pass Filters

15.2 Scaling

15.3 Op Amp Bandpass and Bandreject Filters

15.4 High Order Op Amp Filters

15.5 Narrowband Bandpass and Bandreject Filters 2008 Pearson Education

15.1 First-Order Low-Pass and High-Pass FiltersActive filters consist of op amps, resistors, and capacitors.

They can be configured as low-pass, high-pass, bandpass, and bandreject filters.

2008 Pearson Education

15.1 First-Order Low-Pass and High-Pass Filters

They overcome many of the disadvantages associated with passive filters. 2008 Pearson Education

A first-order low-pass filter 2008 Pearson Education15.1 First-Order Low-Pass and High-Pass Filters

A general op amp circuit 2008 Pearson Education15.1 First-Order Low-Pass and High-Pass Filters

A first-order high-pass filter 2008 Pearson Education15.1 First-Order Low-Pass and High-Pass Filters

A prototype low-pass filter has component values of R1 = R2 = 1 and C = 1F, and it produces a unity passband gain and a cutoff frequency of 1 rad/s. 2008 Pearson Education15.1 First-Order Low-Pass and High-Pass Filters

The prototype high-pass filter has same component values and also produces a unity passband gain and a cut-off frequency of 1 rad/s. 2008 Pearson Education15.1 First-Order Low-Pass and High-Pass Filters

15.2 ScalingMagnitude scaling can be used to alter component values without changing the frequency response of a circuit. 2008 Pearson Education

15.2 ScalingFor a magnitude scale factor of km, the scaled (primed) values of resistance, capacitance, and inductance are 2008 Pearson Education

Frequency scaling can be used to shift the frequency response of a circuit to another frequency region without changing the overall shape of the frequency response.

2008 Pearson Education15.2 Scaling

15.2 ScalingFor a frequency scale factor of kf , the scaled (primed) values of resistance, capacitance, and inductance are 2008 Pearson Education

15.2 ScalingComponents can be scaled in both magnitude and frequency, with the scaled (primed) component values given by

2008 Pearson Education

The design of active low-pass and high-pass filters can begin with a prototype filter circuit.

Scaling can then be applied to shift the frequency response to the desired cutoff frequency, using component values that are commercially available. 2008 Pearson Education15.2 Scaling

15.3 Op Amp Bandpass and Bandreject FiltersConstructing the Bode magnitude plot of a bandpass filter 2008 Pearson Education

A cascaded op amp bandpass filter The block diagram The circuit 2008 Pearson Education15.3 Op Amp Bandpass and Bandreject Filters

An active broadband bandpass filter can be constructed using a cascade of a low-pass filter with the bandpass filters upper cutoff frequency, a high-pass filter with the bandpass filters lower cutoff frequency, and (optionally) an inverting amplifier gain stage to achieve nonunity gain in the passband.

2008 Pearson Education15.3 Op Amp Bandpass and Bandreject Filters

Bandpass filters implemented in this fashion must be broadband filters (c2 c1), so that the elements of the cascade can be specified independently of one another.


Example: Designing a Broadband Bandpass Op Amp Filter. Design a bandpass filter for a graphic equalizer to provide an amplification of 2 within the band of frequencies between 100 and 10,000 Hz. Use 0.2F capacitors.


Constructing the Bode magnitude plot of a bandreject filter 2008 Pearson Education15.3 Op Amp Bandpass and Bandreject Filters

An active broadband bandreject filter can be constructed using a parallel combination of a low-pass filter with the bandreject filters lower cutoff frequency and a high-pass filter with the bandreject filters upper cutoff frequency. 2008 Pearson Education15.3 Op Amp Bandpass and Bandreject Filters

The outputs are then fed into a summing amplifier, which can produce nonunity gain in the passband. 2008 Pearson Education15.3 Op Amp Bandpass and Bandreject FiltersBandreject filters implemented in this way must be broadband filters (c2 c1), so that the low-pass and high-pass filter circuits can be designed independently of one another.

A parallel op amp bandreject filter The block diagram The circuit 2008 Pearson Education15.3 Op Amp Bandpass and Bandreject Filters

15.4 Higher Order Op Amp FiltersThe bode magnitude plot of a cascade of identical prototype first-order filters 2008 Pearson Education

Higher order active filters have multiple poles in their transfer functions, resulting in a sharper transition from the passband to the stopband and thus a more nearly ideal frequency response. 2008 Pearson Education15.4 Higher Order Op Amp Filters

A cascade of identical unity-gain low-pass filters. The block diagram The circuit 2008 Pearson Education15.4 Higher Order Op Amp Filters

The transfer function of an nthorder Butterworth low-pass filter with a cutoff frequency of 1 rad/s can be determined from the equation: 2008 Pearson Education15.4 Higher Order Op Amp Filters

ByFinding the roots of the denominator polynomial.Assigning the left-half plane roots to H(s).Writing the denominator of H(s) as a product of first- and second- order factors. 2008 Pearson Education15.4 Higher Order Op Amp Filters

Defining the transition region for a low-pass filter 2008 Pearson Education15.4 Higher Order Op Amp Filters

15.5 Narrowband Bandpassand Bandreject FiltersAn active high-Q bandpass filter 2008 Pearson Education

A high-Q active bandreject filter 2008 Pearson Education15.5 Narrowband Bandpassand Bandreject Filters

If a high-Q, or narrowband, bandpass, or bandreject filter is needed, the cascade or parallel combination will not work. Instead, the circuits shown previously are used with the appropriate design equations.

2008 Pearson Education15.5 Narrowband Bandpass and Bandreject Filters

THE END 2008 Pearson Education

Documents

ACTIVE FILTERS